4t-1元旋转对称2-弹性函数的构造

杜蛟; 刘春红; 庞善起

doi:10.11959/j.issn.1000-436x.2020213

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4t-1元旋转对称2-弹性函数的构造

学术论文 | 更新时间：2024-06-05

- 4t-1元旋转对称2-弹性函数的构造
- Constructions of rotation symmetric 2-resilient functions with 4t_-1 number of variables
- 通信学报 2020年41卷第11期页码：169-175
- 作者机构：
  
  1. 河南师范大学数学与信息科学学院，河南新乡 453007
  2. 河南师范大学大数据统计与优化控制河南省工程实验室，河南新乡 453007
  3. 河南师范大学计算机与信息工程学院，河南新乡 453007
- 作者简介：
  
  [ "杜蛟（1978- ），男，湖北英山人，博士，河南师范大学副教授、硕士生导师，主要研究方向为现代密码学中的布尔函数与序列设计、编码密码的数学理论" ]
  [ "刘春红（1969- ），女，河南新乡人，博士，河南师范大学副教授、硕士生导师，主要研究方向为云计算安全、云计算资源管理与机器学习、网络空间安全等" ]
  [ "庞善起（1965- ），男，河南卫辉人，博士，河南师范大学教授、博士生导师，主要研究方向为试验设计、量子信息与编码密码的数学理论" ]
- 基金信息：
  
  国家自然科学基金资助项目(11971004);河南省重点研发与推广专项（科技攻关）基金资助项目(202102210163);河南省高等教学改革研究与实践基金资助项目(2019SJGLX033Y);国家级大学生创新创业训练计划基金资助项目(202010476001)
- DOI：10.11959/j.issn.1000-436x.2020213
  中图分类号： TN918.1
- 网络出版日期：2020-11，
  
  纸质出版日期：2020-11-25
- 稿件说明：
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杜蛟, 刘春红, 庞善起. 4t-1元旋转对称2-弹性函数的构造[J]. 通信学报, 2020,41(11):169-175.

Jiao DU, Chunhong LIU, Shanqi PANG. Constructions of rotation symmetric 2-resilient functions with 4t_-1 number of variables[J]. Journal on communications, 2020, 41(11): 169-175.
杜蛟, 刘春红, 庞善起. 4t-1元旋转对称2-弹性函数的构造[J]. 通信学报, 2020,41(11):169-175. DOI： 10.11959/j.issn.1000-436x.2020213.

Jiao DU, Chunhong LIU, Shanqi PANG. Constructions of rotation symmetric 2-resilient functions with 4t_-1 number of variables[J]. Journal on communications, 2020, 41(11): 169-175. DOI： 10.11959/j.issn.1000-436x.2020213.

摘要

在特征为2的有限域F

上的n维线性空间

中，给出了旋转对称轨道的若干性质，定义了旋转对称轨道的数对00、01和11的分布矩阵，给出了一个2-弹性旋转对称函数的新刻画，通过修改已有的线性旋转对称弹性函数f

(x)=x

+…+x

的支撑集（其中n=4t-1），给出了一个基于轨道交换技术的一类4t-1元旋转对称2-弹性函数的构造方法，并通过实例说明了所提构造方法的思想。

Abstract

Some properties of rotation symmetric orbits were proposed in n dimensional vector space over finite field of characteristic 2

a matrix on the distributions of number pairs such as 00

01 and 11 was defined

and a new characterization of 2-resilient rotation symmetric functions was introduced.Constructions of rotation symmetric 2-resilient Boolean functions with 4t-1 number of variables were presented by modifying the support of the linear rotation symmetric functions

such as f

(x)=x

+…+x

where n=4t-1.At last

an example was demonstrated to introduce the spirit of the proposed method to construct 2-resilient rotation symmetric functions with 4t-1 number of variables.

关键词

Keywords

references

PIEPRZYK J , QU C X . Fast hashing and rotation symmetric functions [J ] . Journal Universal Computer Science , 1999 , 5 ( 1 ): 20 - 31 .

FILIOL E , FONTAINE C . Highly nonlinear balanced boolean functions with a good correlation-immunity [C ] // International Conference on the Theory and Application of Cryptographic Techniques . Berlin:Springer , 1998 : 475 - 488 .

CUSICK W , STANICA P , MAITRA S . Fast evaluation,weight and nonlinearity of rotation symmetric functions [J ] . Discrete Mathematics , 2002 , 258 ( 1-3 ): 289 - 301 .

STANICA P , MAITRA S , CLARK J . Results on rotation symmetric bent and correlation immune Boolean functions [C ] // Fast Software Encryption Workshop (FSE 2004) . Berlin:Springer , 2004 : 161 - 177 .

KAVUT S , MAITRA S , SARKAR S , et al . Enumeration of 9-variable Rotation symmetric Boolean functions having nonlinearity>240 [C ] // International Conference on Cryptology . Berlin:Springer , 2006 : 266 - 279 .

KAVUT S , MAITRA S , YUCEL M D . Search for Boolean functions with excellent profiles in the rotation symmetric class [J ] . IEEE Transactions on Information Theory , 2007 , 53 ( 5 ): 1743 - 1751 .

CARLET C , DALAI D K , GUPTA K C , et al . Algebraic immunity for cryptographically significant Boolean functions:analysis and construction [J ] . IEEE Transactions on Information Theory , 2006 , 52 ( 7 ): 3105 - 3121 .

STANICA P , MAITRA S . Rotation symmetric Boolean functions count and cryptographic properties [J ] . Discrete Applied Mathematics , 2008 , 156 : 1567 - 1580 .

王永娟 , 韩文报 , 李世取 . 满足 CI 的 RotS 函数的构造与计数 [J ] . 通信学报 , 2007 , 28 ( 11 ): 6 - 9 .

WANG Y J , HAN W B , LI S Q . Construction and numeration of correlation immunity RotS Boolean function [J ] . Journal on Communications , 2007 , 28 ( 11 ): 6 - 9 .

FU S J , LI C , QU L J . On the number of rotation symmetric Boolean functions [J ] . Science China Information Sciences , 2010 , 53 ( 3 ): 537 - 545 .

张鹏 , 付绍静 , 屈龙江 , 等 . 平衡旋转对称布尔函数的计数 [J ] . 应用科学学报 , 2012 , 30 ( 1 ): 45 - 51 .

ZHANG P , FU S J , QU L J , et al . Enumeration of balanced rotation-symmetric Boolean functions [J ] . Journal of Applied Sciences-Electronics and Information Engineering , 2012 , 30 ( 1 ): 45 - 51 .

庞善起 , 杜蛟 , 席金彦 . 相关免疫函数阶的判别方法 [J ] . 应用数学学报 , 2009 , 32 ( 3 ): 445 - 453 .

PANG S Q , DU J , XI J Y . Some methods for judging the order of correlation-immune functions [J ] . Acta Mathematicae Applicatae Sinica , 2009 , 32 ( 3 ): 445 - 453 .

杜蛟 , 温巧燕 , 张劼 , 等 . 素数元旋转对称弹性布尔函数的构造与计数 [J ] . 通信学报 , 2013 , 34 ( 3 ): 6 - 13 .

DU J , WEN Q Y , ZHANG J , et al . Construction and count of resilient rotation symmetric Boolean functions with prime number of variables [J ] . Journal on Communications , 2013 , 34 ( 3 ): 6 - 13 .

SUN L , FU F W , GUANG X . Two classes of 1-resilient prime-variable rotation symmetric Boolean functions [J ] . IEICE Transactions on Fundamentals of Electronics Communications ＆ Computer Sciences , 2017 , 100 ( 3 ): 902 - 907 .

DU J , WEN Q Y , ZHANG J , et al . Constructions of resilient rotation symmetric Boolean functions on given number of variables [J ] . IET Information Security , 2014 , 8 ( 5 ): 265 - 272 .

杜蛟 , 温巧燕 , 张劼 , 等 . 2p元2-阶旋转对称弹性布尔函数的构造与计数 [J ] . 北京邮电大学学报 , 2013 , 35 ( 5 ): 36 - 40 .

DU J , WEN Q Y , ZHANG J , et al . Construction and counting of resilient 2-rotation symmetric Boolean functions with 2p variables [J ] . Journal of Beijing University of Posts and Telecommunications , 2013 , 35 ( 5 ): 36 - 40 .

PANG S Q , WANG X N , WANG J , et al . Construction and count of 1-resilient rotation symmetric Boolean functions [J ] . Information Sciences , 2018 , 450 : 336 - 342 .

SUN L , LIU J , FU F W . Secondary constructions of RSBFs with good cryptographic properties [J ] . Information Processing Letters , 2019 , 147 : 44 - 48 .

杜蛟 , 庞善起 , 温巧燕 , 等 . GF(p)上q元旋转对称弹性函数的一个等价刻画 [J ] . 通信学报 , 2014 , 35 ( 8 ): 179 - 183 .

DU J , PANG S Q , WEN Q Y , et al . Equivalent characterization of resilient rotation symmetric functions with q number of variables over GF(p) [J ] . Journal on Communications , 2014 , 35 ( 8 ): 179 - 183 .

DU J , FU S J , QU L J , et al . New constructions of q-variable 1-resilient rotation symmetric functions over F p [J ] . Science China Information Science , 2016 , 59 ( 7 ): 1 - 3 .

SU S H , TANG X H . Systematic constructions of rotation symmetric bent functions,2-rotation symmetric bent functions,and bent idempotent functions [J ] . IEEE Transactions on Information Theory , 63 ( 7 ): 4658 - 4667 .

GOPALAKRISHNAN K , STINSON D R . Three characterizations of non-binary correlation-immune and resilient functions [J ] . Designs Codes ＆ Cryptography , 1995 , 5 : 241 - 251 .

STINSON D R . Resilient functions and large sets of orthogonal arrays [J ] . Congressus Numerantium , 1993 , 92 : 105 - 110 .

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