8元多输出旋转对称弹性函数的构造与计数

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

通信学报 ›› 2017, Vol. 38 ›› Issue (7): 47-55.doi: 10.11959/j.issn.1000-436x.2017140

8元多输出旋转对称弹性函数的构造与计数

杜蛟¹,尚玉婧¹,赵金玲¹,董乐¹,张恩²

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

修回日期:2017-05-17 出版日期:2017-07-01 发布日期:2017-08-25
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。
基金资助:
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)

Construction and count of multi-output rotation symmetric resilient functions with 8 input variables

Jiao DU¹,Yu-jing SHANG¹,Jin-ling ZHAO¹,Le DONG¹,En ZHANG²

¹ College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China
² College of Computer and Information Engineering,Henan Normal University,Xinxiang 453007,China

Revised:2017-05-17 Online:2017-07-01 Published:2017-08-25
Supported by:
The National Natural Science Foundation of China(U1404601);The National Natural Science Foundation of China(11571094);The National Natural Science Foundation of China(61402154);The National Natural Science Foundation of China(U1604156);PhD Research Startup Foundation of Henan Normal University(5101019170133)

摘要/Abstract

摘要：

在2^r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。

关键词: 密码学, 旋转对称函数, 平衡函数, 弹性函数, 支撑矩阵

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^rinput 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.

Key words: cryptography, rotation symmetric function, balanced function, resilient function, support table

中图分类号:

TN918.1

杜蛟,尚玉婧,赵金玲,董乐,张恩. 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,Le DONG,En ZHANG. Construction and count of multi-output rotation symmetric resilient functions with 8 input variables[J]. Journal on Communications, 2017, 38(7): 47-55.

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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

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