8元多输出旋转对称弹性函数的构造与计数

杜蛟; 尚玉婧; 赵金玲; 董乐; 张恩

doi:10.11959/j.issn.1000-436x.2017140

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8元多输出旋转对称弹性函数的构造与计数

学术论文 | 更新时间：2024-06-05

- 8元多输出旋转对称弹性函数的构造与计数
- Construction and count of multi-output rotation symmetric resilient functions with 8 input variables
- 通信学报 2017年38卷第7期页码：47-55
- 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，河南师范大学讲师，主要研究方向为密码学与应用数学。" ]
  [ "尚玉婧（1993-），女，河南卫辉人，河南师范大学硕士生，主要研究方向为应用数学。" ]
  [ "赵金玲（1994-），女，河南商丘人，河南师范大学硕士生，主要研究方向为应用数学。" ]
  [ "董乐（1980-），男，河南封丘人，博士，河南师范大学副教授，主要研究方向为分组密码的设计与分析。" ]
  [ "张恩（1974-），男，河南新乡人，博士，河南师范大学副教授，主要研究方向为密码协议与云计算安全。" ]
- 基金信息：
  
  国家自然科学基金资助项目(U1404601);国家自然科学基金资助项目(11571094);国家自然科学基金资助项目(61402154);国家自然科学基金资助项目(U1604156);河南师范大学博士科研启动基金资助项目(5101019170133)
- DOI：10.11959/j.issn.1000-436x.2017140
  中图分类号： TN918.1
- 网络出版日期：2017-07，
  
  纸质出版日期：2017-07-25
- 稿件说明：
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杜蛟, 尚玉婧, 赵金玲, 等. 8元多输出旋转对称弹性函数的构造与计数[J]. 通信学报, 2017,38(7):47-55.

Jiao DU, Yu-jing SHANG, Jin-ling ZHAO, et al. Construction and count of multi-output rotation symmetric resilient functions with 8 input variables[J]. Journal on communications, 2017, 38(7): 47-55.
杜蛟, 尚玉婧, 赵金玲, 等. 8元多输出旋转对称弹性函数的构造与计数[J]. 通信学报, 2017,38(7):47-55. DOI： 10.11959/j.issn.1000-436x.2017140.

Jiao DU, Yu-jing SHANG, Jin-ling ZHAO, et al. Construction and count of multi-output rotation symmetric resilient functions with 8 input variables[J]. Journal on communications, 2017, 38(7): 47-55. DOI： 10.11959/j.issn.1000-436x.2017140.

摘要

在2

个变元的多输出旋转对称平衡函数和弹性函数存在的条件下，研究了输出变量维数的取值问题。根据输出变量的不同维数，基于弹性函数和

正交表大集间的等价关系，给出了8元多输出平衡函数的计数结果，在此基础上进一步研究了8元多输出旋转对称1-弹性函数的构造与计数方法，将这类函数的构造问题转化为方程组的求解问题。

Abstract

The value ranges of the number of output variables were determined respectively under the existence of multi-output rotation symmetric balanced functions and resilient functions with 2

input variables.Based on the equivalence between the resilient functions and large sets of orthogonal arrays

some results on the construction and count of multi-output rotation symmetric balanced functions with 8 input variables were presented according to the different dimensions of output vectors

and construction and count of multi-output rotation symmetric 1-resilient functions with 8 input variables were also studied.Besides

constructions of multi-output rotation symmetric resilient functions are transformed into the problem of solving a system of equations.

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references

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