检索结果-内蒙古大学图书馆

Constructing balanced 2p-variable rotation symmetric boolean functions with optimal algebraic immunity, high nonlinearity and high algebraic degree

引用

DISCRETE MATHEMATICS 2025年第8期348卷

作者： Du, Jiao Chen, Xiaoting Mao, Yongxia Gao, Qiang Wang, Tianyin Henan Normal Univ Henan Engn Lab Big Data Stat Anal & Optimal Contro Xinxiang 453007 Peoples R China Natl Univ Def Technol Coll Sci Changsha 410073 Peoples R China Luoyang Normal Univ Fac Math Sci Luoyang 471934 Peoples R China

How to design cryptographic boolean functions is a challenge work in the design of stream and block ciphers. Cryptographic criteria of boolean functions are connected with some known cryptanalytic attacks. To resist these known attacks, it is important to search boolean functions with some properties, including balancedness, optimal algebraic immunity, high algebraic degree, good nonlinearity, high correlation immunity, etc. rotation symmetric boolean functions (RSBFs) can have these properties simultaneously. In this paper, we propose a new class of balanced 2p-variable RSBFs based on the compositions of an integer, where pis an odd prime. It is found that the functions of this class have optimal algebraic immunity, and their nonlinearity reaches 22p-1 - (2p-1 ) + 2 p-2 i=3 (i - 1) (i - 2) ( p-2 ) + N eta + 1 (where N eta = p-2-(p mod 4) and p is an odd prime), which is higher than the previously constructed balanced even-variable RSBFs with optimal algebraic immunity. At the same time, the algebraic degree of the constructed functions are studied, and the results show that they can be optimal under certain conditions. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： rotation symmetric boolean functions Algebraic immunity Nonlinearity Algebraic degree

来源：评论

学校读者我要写书评

暂无评论

rotation symmetric boolean functions - Count and cryptographic properties

引用

DISCRETE APPLIED MATHEMATICS 2008年第10期156卷 1567-1580页

作者： Stanica, Pantelimon Maitra, Subhamoy USN Postgrad Sch Dept Appl Math GSEAS Monterey CA 93943 USA Indian Stat Inst Appl Stat Unit Kolkata 700108 India

rotation symmetric (RotS) boolean functions have been used as components of different cryptosystems. This class of boolean functions are invariant under circular translation of indices. Using Burnside's lemma it can be seen that the number of n-variable rotation symmetric boolean functions is 2(gn), where g(n) = (t/n)Sigma(t\n) phi(t)2(n/t), and phi(.) is the Euler phi-function, In this paper, we find the number of short and long cycles of elements in F-2(n) having fixed weight, under the RotS action. As a consequence we obtain the number of homogeneous RotS functions having algebraic degree w. Our results make the search space of RotS functions much reduced and we successfully analyzed important cryptographic properties of such functions by executing computer programs. We study RotS bent functions up to 10 variables and observe (experimentally) that there is no homogeneous rotation symmetric bent function having degree > 2. Further, we studied the RotS functions on 5, 6, 7 variables by computer search for correlation immunity and propagation characteristics and found some functions with very good cryptographic properties which were not known earlier. (C) 2007 Elsevier B.V. All rights reserved.

关键词： rotation symmetric boolean functions enumeration correlation immunity resiliency algebraic degree nonlinearity autocorrelation

来源：评论

学校读者我要写书评

暂无评论

rotation symmetric boolean functions -;Count and Cryptographic Properties

引用

Electronic Notes in Discrete Mathematics 2003年 15卷 139-145页

作者： Stǎnicǎ, Pantelimon Maitra, Subhamoy Department of Mathematics Auburn University Montgomery Montgomery AL 36124-4023 United States Applied Statistics Unit Indian Statistical Institute 203 Calcutta 700 108 B. T. Road India

In 1999, Pieprzyk and Qu presented rotation symmetric (RotS) functions as components in the rounds of hashing algorithm. Later, in 2002, Cusick and Stǎnicǎ presented further advancement in this area. This class of boolean functions are invariant under circular translation of indices. In this paper, using Burnside's lemma, we prove that the number of n-variable rotation symmetric boolean functions is 2^gn, where g_n and φ is the Euler phi-function. Moreover, we find the number of short and long cycles of elements in Zⁿ₂ having fixed weight, under the RotS action. As a consequence we obtain the number of homogeneous RotS functions having algebraic degree w. Our results make the search space of RotS functions much reduced and we successfully analyzed important cryptographic properties of such functions by executing computer programs. We found that there are exactly 8, 48, and 15104, RotS bent functions on 4, 6, and 8 variables respectively. Experimental results up to 10 variables show that there is no homogeneous rotation symmetric bent function with degree > 2. Further, we studied the RotS functions on 5, 6, 7 variables for correlation immunity and propagation characteristics and found some functions with very good cryptographic properties which were not known earlier. © 2005 Elsevier Ltd. All rights reserved.

关键词： Algebraic Degree Autocorrelation Correlation Immunity Enumeration Nonlinearity Resiliency rotation symmetric boolean functions

来源：评论

学校读者我要写书评

暂无评论

Construction and Count of 1-Resilient rotation symmetric boolean functions on 4p Variables

引用

Chinese Journal of Electronics 2017年第6期26卷 1276-1283页

作者： PANG Shanqi XU Wenju DU Jiao WANG Ying College of Mathematics and Information Science Henan Normal University

This paper studies the properties of orbit matrix and gives a formula to compute the number of these orbit matrices on 4p variables, where p is an odd prime. It has been demonstrated that the construction of 1-resilient rotation symmetric boolean functions(RSBFs) on 4p variables is equivalent to solving an equation system. By the proposed method, all 1-resilient RSBFs on 12 variables can be constructed. We present a counting formula for the total number of all 1-resilient RSBFs on 4p variables. As application of our method, some 1-resilient RSBFs on 12 variables are presented.

关键词： Cryptography rotation symmetric boolean functions Orbit matrix Resilient functions

来源：评论

学校读者我要写书评

暂无评论

A new construction of odd-variable rotation symmetric boolean functions with optimal algebraic immunity and higher nonlinearity

引用

THEORETICAL COMPUTER SCIENCE 2021年 887卷 152-163页

作者： Su, Sihong Li, Jingjing Wang, Bingxin Henan Univ Sch Math & Stat Kaifeng 475004 Peoples R China Henan Univ Henan Engn Res Ctr Artificial Intelligence Theory Kaifeng 475004 Peoples R China

rotation symmetric boolean functions are potentially rich in functions of cryptographic significance. In this paper, a new construction of odd-variable rotation symmetric boolean functions with optimal algebraic immunity is presented. By a direct calculation, the nonlinearity of the newly constructed functions is higher than the nonlinearities of all the known odd-variable rotation symmetric boolean functions with optimal algebraic immunity. The algebraic degree and the fast algebraic immunity of our functions are also considered. (C) 2021 Elsevier B.V. All rights reserved.

关键词： rotation symmetric boolean functions Algebraic immunity Walsh transform Nonlinearity Algebraic degree

来源：评论

学校读者我要写书评

暂无评论

Constructions of rotation symmetric boolean functions satisfying almost all cryptographic criteria

引用

THEORETICAL COMPUTER SCIENCE 2024年 1020卷

作者： Sun, Lei Shi, Zexia Liu, Jian Fu, Fang-Wei Hebei Univ Econ & Business Sch Management Sci & Informat Engn Shijiazhuang 050061 Peoples R China Hebei Univ Econ & Business Hebei Cross Border Ecommerce Technol Innovat Ctr Shijiazhuang 050061 Peoples R China Hebei Normal Univ Sch Math Sci Shijiazhuang 050010 Peoples R China Tianjin Univ Coll Intelligence & Comp Tianjin 300350 Peoples R China Nankai Univ Chern Inst Math Tianjin 300071 Peoples R China

Constructions of boolean functions with various cryptographic properties have always been an important challenge in cryptography. This paper proposes systematic constructions of even- variable rotation symmetric boolean functions satisfying almost all cryptographic criteria, that is, resiliency, optimal algebraic degree, strict avalanche criterion, high nonlinearity, nonexistence of nonzero linear structures, good global avalanche characteristics. Moreover, some of the constructions also have high algebraic immunity. This is the first time that boolean functions having such cryptographic properties are obtained, which can be considered as good candidates for the design of real-life encryption schemes.

关键词： rotation symmetric boolean functions Resilient Strict avalanche criterion Nonlinearity Algebraic degree Stream cipher

来源：评论

学校读者我要写书评

暂无评论

Generalized Walsh transforms of symmetric and rotation symmetric boolean functions are linear recurrent

引用

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2018年第5期29卷 433-453页

作者： Castro, Francis N. Medina, Luis A. Stanica, Pantelimon Univ Puerto Rico Dept Math San Juan PR 00936 USA Naval Postgrad Sch Dept Appl Math Monterey CA 93943 USA

Exponential sums of symmetric boolean functions are linear recurrent with integer coefficients. This was first established by Cai, Green and Thierauf in the mid nineties. Consequences of this result has been used to study the asymptotic behavior of symmetric boolean functions. Recently, Cusick extended it to rotation symmetric boolean functions, which are functions with good cryptographic properties. In this article, we put all these results in the general context of Walsh transforms and some of its generalizations (nega-Hadamard transform, for example). Precisely, we show that Walsh transforms, for which exponential sums are just an instance, of symmetric and rotation symmetric boolean functions satisfy linear recurrences with integer coefficients. We also provide a closed formula for the Walsh transform and nega-Hadamard transform of any symmetric boolean functions. Moreover, using the techniques presented in this work, we show that some families of rotation symmetric boolean functions are not bent when the number of variables is sufficiently large and provide asymptotic evidence to a conjecture of Stnic and Maitra.

关键词： Walsh transform Nega-Hadamard transform symmetric boolean functions rotation symmetric boolean functions Linear recurrences

来源：评论

学校读者我要写书评

暂无评论

Balanced rotation symmetric boolean functions With Good Autocorrelation Properties

引用

IEEE ACCESS 2021年 9卷 67850-67858页

作者： Sun, Lei Shi, Zexia Hebei Univ Econ & Business Coll Informat Technol Shijiazhuang 050061 Hebei Peoples R China Hebei Normal Univ Sch Math Sci Shijiazhuang 050024 Hebei Peoples R China

rotation symmetric boolean functions (RSBFs) are used widely in symmetric cryptography. In this paper, a systematic construction of balanced odd-variable RSBFs satisfying strict avalanche criterion is proposed. Hence, a class of (6k + 3)-variable resilient RSBFs satisfying strict avalanche criterion is also presented for any k >= 2. Some of the obtained RSBFs have many other good cryptographic properties at the same time, that is, optimal algebraic degree, good global avalanche characteristics, high nonlinearity and nonexistence of nonzero linear structures. Moreover, we obtain some count results of RSBFs satisfying strict avalanche criterion. This is the first time that the autocorrelation properties of RSBFs are investigated systemically.

关键词： Cryptography global avalanche characteristics resilient rotation symmetric boolean functions strict avalanche criterion

来源：评论

学校读者我要写书评

暂无评论

Construction of odd-Variable rotation symmetric boolean functions with Maximum Algebraic Immunity

引用

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2016年第4期E99A卷 853-855页

作者： Fu, Shaojing Du, Jiao Qu, Longjiang Li, Chao Natl Univ Def Technol Coll Comp Changsha Hunan Peoples R China Beijing Univ Posts & Telecommun State Key Lab Networking & Switching Technol Beijing Peoples R China Natl Univ Def Technol Dept Math & Syst Sci Changsha Hunan Peoples R China Henan Normal Univ Coll Math & Informat Sci Xinxiang Peoples R China

rotation symmetric boolean functions (RSBFs) that are invariant under circular translation of indices have been used as components of different cryptosystems. In this paper, odd-variable balanced RSBFs with maximum algebraic immunity (AI) are investigated. We provide a construction of n-variable (n = 2k + 1 odd and n >= 13) RSBFs with maximum AI and nonlinearity >= 2(n-1) - ((n-1)(k)) + 2(k) + 2(k-2) - k, which have nonlinearities significantly higher than the previous nonlinearity of RSBFs with maximum AI.

关键词： cryptography rotation symmetric boolean functions algebraic immunity nonlinearity

来源：评论

学校读者我要写书评

暂无评论

New Construction of Even-variable rotation symmetric boolean functions with Optimum Algebraic Immunity

引用

INTERNATIONAL JOURNAL OF SECURITY AND ITS APPLICATIONS 2014年第1期8卷 307-318页

作者： Chen, Yindong Xiang, Hongyan Zhang, Ya-nan Shantou Univ Coll Engn Shantou 515063 Peoples R China

The rotation symmetric boolean functions which are invariant under the action of cyclic group have been used as components of different cryptosystems. In order to resist algebraic attacks, boolean functions should have high algebraic immunity. This paper studies the construction of even-variable rotation symmetric boolean functions with optimum algebraic immunity. We construct ([ n/4] - 3) different rotation symmetric boolean functions which achieve both optimum algebraic immunity and high nonlinearity when an even n (n >= 16) . is given.

关键词： Algebraic attacks rotation symmetric boolean functions Algebraic immunity

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：