<italic style="font-style: italic">k</italic>-阶旋转对称2-弹性函数的构造

刘春红; 李龙飞; 高强; 王天银; 杜蛟; 庞善起

doi:10.12263/DZXB.20240833

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k-阶旋转对称2-弹性函数的构造

学术论文 | 更新时间：2025-08-18

- k-阶旋转对称2-弹性函数的构造
- Concrete Constructions of k-Rotation Symmetric 2-Resilient Boolean Functions
- 电子学报 2025年53卷第5期页码：1445-1452
- 作者机构：
  
  1.河南师范大学计算机与信息工程学院，河南新乡 453007
  2.河南师范大学数学与统计学院，河南新乡 453007
  3.洛阳师范学院数学科学学院，河南洛阳 471934
- 作者简介：
  
  [ "刘春红女，1969年生.博士，现为河南师范大学教授、硕士生导师.主要研究方向为智能服务计算、云计算安全和隐私保护.E-mail: lch@htu.edu.cn" ]
  [ "李龙飞男，2000年生.现为河南师范大学硕士研究生.主要研究方向为编码密码的数学理论.E-mail: 1429785915@qq.com" ]
  [ "高强男，1986年生.博士，现为河南师范大学讲师.主要研究方向为组合设计、无线传感器网络密钥预分发方案设计、密码函数的设计与安全性指标分析.E-mail: gaoqiang8612@126.com" ]
  [ "王天银男，1979年生.博士，现为洛阳师范学院教授，河南师范大学兼职博士生导师.主要研究方向为密码学、隐私保护.E-mail: wangtianyin79@163.com" ]
  [ "杜蛟男，1978年生.博士，现为河南师范大学副教授、博士生导师.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.E-mail: jiaodudj@126.com" ]
  [ "庞善起男，1965年生.博士，现为河南师范大学教授、博士生导师.主要研究方向为试验设计、组合设计、编码密码的数学理论.E-mail: pangshanqi@263.net" ]
- 基金信息：
  
  国家自然科学基金(62372157;62272208;62172196;12471245)
- DOI：10.12263/DZXB.20240833
  中图分类号： TN918.1;
- 收稿：2024-09-11，
  
  修回：2025-03-09，
  
  纸质出版：2025-05-25
- 稿件说明：
移动端阅览
刘春红, 李龙飞, 高强, 等. k-阶旋转对称2-弹性函数的构造[J]. 电子学报, 2025, 53(05): 1445-1452.

LIU Chun-hong, LI Long-fei, GAO Qiang, et al. Concrete Constructions of k-Rotation Symmetric 2-Resilient Boolean Functions[J]. Acta Electronica Sinica, 2025, 53(05): 1445-1452.
刘春红, 李龙飞, 高强, 等. k-阶旋转对称2-弹性函数的构造[J]. 电子学报, 2025, 53(05): 1445-1452. DOI：10.12263/DZXB.20240833

LIU Chun-hong, LI Long-fei, GAO Qiang, et al. Concrete Constructions of k-Rotation Symmetric 2-Resilient Boolean Functions[J]. Acta Electronica Sinica, 2025, 53(05): 1445-1452. DOI：10.12263/DZXB.20240833

摘要

基于支撑集交换技术，通过对

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87902841&type=

2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87902842&type=

1.60866666

-阶旋转对称轨道的分析，给出了一个由

元1-阶旋转对称轨道，得到

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2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87902843&type=

3.13266683

元

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2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87902842&type=

1.60866666

-阶旋转对称轨道的方法.进一步，通过改变定义在

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3.38666677

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3.80999994

上的旋转对称弹性函数的支撑集，构造出新的

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2.28600001

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1.60866666

-阶旋转对称2-弹性函数，且至少能得到

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2.53999996

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87902846&type=

5.67266655

个不同的

</mo><mi>k</mi><mo>≥</mo><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo></math>

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2.96333337

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17.86466599

元

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2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87902842&type=

1.60866666

-阶旋转对称2-弹性函数.

Abstract

Based on the techniques of the support set exchange

the orbits of

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2.28600001

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3.13266683

-variable

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2.28600001

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1.60866666

-rotation symmetric can be obtained from the orbits of

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2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87902874&type=

1.60866666

-variable 1-rotation symmetric through the analysis of the orbits of

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2.28600001

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1.60866666

-rotation symmetric.Furthermore

by modifying the support set of the rotation symmetric functions over

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3.38666677

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87902861&type=

3.80999994

a new class of

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2.28600001

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1.60866666

-rotation symmetric 2-resilient Boolean functions are constructed and at least

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2.53999996

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5.67266655

different

</mo><mi>k</mi><mo>≥</mo><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87902908&type=

2.96333337

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87902890&type=

17.86466599

-variable

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2.28600001

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1.60866666

-rotation symmetric 2-resilient Boolean functions can be obtained.

关键词

Keywords

references

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李泉 , 高光谱 , 刘文芬 . <math id="M488"><mi>k</mi></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87904871&type= 2.28600001 https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87904886&type= 1.60866666 -阶旋转对称函数性质分析与轨道计数 [J ] . 通信学报 , 2012 , 33 ( 1 ): 114 - 119 .

LI Q , GAO G P , LIU W F . Analysis of properties and orbital counting for <math id="M489"><mi>k</mi></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87904905&type= 2.28600001 https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=87904887&type= 1.60866666 -Order rotational symmetry functions [J ] . Journal on Communications , 2012 , 33 ( 1 ): 114 - 119 . (in Chinese)

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 , 2012 , 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 , 2012 , 35 ( 5 ): 36 - 40 . (in Chinese)

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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 .

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杜蛟 , 李琳 , 赵紫薇 , 等 . 7元旋转对称2-弹性函数的构造 [J ] . 通信学报 , 2024 , 45 ( 1 ): 194 - 200 .

DU J , LI L , ZHAO Z W , et al . Concrete constructions of 2-resilient rotation symmetric Boolean functions with 7 variables [J ] . Journal on Communications , 2024 , 45 ( 1 ): 194 - 200 . (in Chinese)

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k-阶旋转对称2-弹性函数的构造

Concrete Constructions of k-Rotation Symmetric 2-Resilient Boolean Functions

DOI：10.12263/DZXB.20240833

摘要

Abstract

关键词

Keywords

references