基于线性等重码构造严格多输出高原函数  

Construction of Strict Multi-Output Plateaued Functions based on Linear Constant Weight Codes

作　　者：谯通旭[1] 邓雷升[1] 赵中军[1] 王坚[1] 孙瑞[1] QIAO Tong-xu DENG Lei-sheng ZHAO Zhong-jun WANG Jian SUN Rui(No.30 Institute of China Electronics Technology Group Corporation, Chengdu Sichuan 610041, China)

机构地区：[1]中国电子科技集团公司第三十研究所,四川成都610041

出　　处：《通信技术》2017年第4期771-774,共4页Communications Technology

基　　金：国家自然科学基金(No.61309034)~~

摘　　要：多输出高原函数在密码学中具有重要作用。给出它的一个子类,即严格多输出高原函数的定义,则完全非线性函数以及几乎Bent函数均为严格多输出高原函数,在密码学中有很好的应用。基于Walsh-Hadamard码,构造具有最大码字重量R_k的(n,k)线性等重码,证明R_k≥R_(k+1),并给出了R_k=R_(k+1)的充分必要条件。此外,基于线性等重码,构造二次严格多输出高原函数,同时计算这些严格多输出高原函数的非线性度。Multi-output plateaued functions play an important role in cryptography.The strict multi-output plateaued functions, as are a subclass of multi-output plateaued functions is defined. Both perfect nonlinear function and almost Bent function are strict multi-output plateaued functions .These functions are well applied to cryptography. Based on Walsh-Hadamard code,linear （n,k） constant weight code with maximum code weight Rk is constructed.h is also proved that Rk is greater than or equal to Rk＋1.The sufficient and necessary condition Of Rk equating Rk＋1 is given.Based on linear constant weight codes, strict multi-output plateaued functions with algebraic degree 2 are constructed.The nonlinearity of these strict multi-output plateaued functions is also computed.

关 键 词：严格多输出高原函数 线性等重码 Walsh-Hadamard码 WALSH谱 非线性度 

分 类 号：TN918.1[电子电信—通信与信息系统]