基于拉丁方的GF(p)上q元旋转对称弹性函数的新构造  

New Constructions of q-Variable Rotation Symmetric Resilient Functions Based on Latin Square Over GF( p)

作　　者：杜蛟[1,2] 刘春红[3] 张恩[3] 尚玉婧 董乐[1,2] DU Jiao;LIU Chun-hong;ZHANG En;SHANG Yu-jing;DONG Le(College of Mathematics and Information Science,Henan Normal University,Xinxiang,Henan 453007,China;;Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control,Henan Normal University,Xinxiang,Henan 453007,China;College of Computer and Information Engineering,Henan Normal University,Xinxiang,Henan 453007,China)

机构地区：[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分析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

出　　处：《电子学报》2018年第9期2173-2180,共8页Acta Electronica Sinica

基　　金：国家自然科学基金(No.U1404601;No.11571094;No.11501181;No.U1604156;No.61402154);河南省科技攻关计划项目(No.172102210045);河南师范大学博士科研启动基金资助项目(No.5101019170133)

摘　　要：在特征为p的有限域上,基于弹性函数与正交表大集间的等价关系,借助于一个具有最大圈结构的拉丁方,给出了一个构造q元旋转对称弹性函数的新方法.此外,通过一个具体的实例说明了本文的方法能够构造出已有方法不能构造的GF(p)上的q元旋转对称弹性函数.A novel method to construct rotation symmetric resilient functions with q variables is proposed over GF(p)by using a Latin square with maximum cycle structure.This method is based on the equivalence between resilient functions and Large sets of orthogonal arrays.Additionally,an example is given to demonstrate that some rotation symmetric resilient functions with q variables can be constructed by the method presented in this paper,while these functions cannot be determined according to the earlier constructions over the finite field GF(p).

关 键 词：密码学 旋转对称函数 平衡函数 弹性函数 l值支撑矩阵 

分 类 号：TN918.1[电子电信—通信与信息系统]