一类新的逐重量完美平衡布尔函数的构造  

A new construction of weightwise perfectly balanced Boolean functions

作　　者：赵庆兰[1,2] 李梦苒 李盼 郑东 ZHAO Qinglan;LI Mengran;LI Pan;ZHENG Dong(School of Cyberspace Security,Xi’an University of Posts and Telecommunications,Xi’an 710121,China;National Engineering Laboratory for Wireless Security,Xi’an 710121,China)

机构地区：[1]西安邮电大学网络空间安全学院,陕西西安710121 [2]无线网络安全技术国家工程研究中心,陕西西安710121

出　　处：《西安邮电大学学报》2024年第4期67-74,共8页Journal of Xi’an University of Posts and Telecommunications

基　　金：国家自然科学基金项目(61902314)。

摘　　要：对逐重量完美平衡(Weightwise Perfectly Balanced,WPB)函数的构造进行研究。给出一类四次函数,分析其k-重量,通过修改四次函数的支撑集完成一类新WPB函数的构造,并对其完美平衡性和代数次数进行证明。利用计算机程序对所构造的小变元WPB函数的k-重量非线性度进行计算,结果表明,构造的一类新WPB函数在某些重量k的子集上与现有函数相比有所提高。A study on the construction of weightwise perfectly balanced(WPB)functions has been conducted.A class of quartic function is given and its k-weight is analyzed.A new class of WPB functions is constructed by modifying the support of the class quadratic functions,and its weightwise perfect balancedness and algebraic degree are proved.The k-weight nonlinearity of small-variable WPB functions is calculated by computer program,and the results indicate that for the constructed new WPB functions,there are some improvements in certain weight k subsets compared with the existing functions.

关 键 词：布尔函数 FLIP 逐重量完美平衡函数 代数次数 k-重量非线性度 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]