通信学报2025，Vol.46Issue(2)：97-107,11.DOI:10.11959/j.issn.1000-436x.2025030
逐重量完美平衡布尔函数的构造
Construction of weightwise perfectly balanced Boolean functions
摘要
Abstract
In the context of homomorphic-friendly stream ciphers such as FLIP,weightwise perfectly balanced Boolean functions have become a hot topic in cryptography in recent years.The k-weight nonlinearity of weightwise perfectly bal-anced Boolean functions constructed by existing research is still far from its upper bound.Based on this,a new construc-tion of weightwise perfectly balanced Boolean functions was introduced.Initially,for positive integers m≥4,a class of 2m-variable Boolean functions with algebraic degree 8 was given,and their k-weight distribution was determined using alge-braic normal forms.Subsequently,by modifying the support set of these basic functions,a class of 2m-variable weight-wise perfectly balanced Boolean functions was constructed.It was theoretically proven that they were balanced on every nontrivial subset with the same weight vector.Additionally,the difference between the construction methods presented and those of similar constructions was analyzed.The algebraic degree of the weightwise perfectly balanced Boolean functions is proven.Compared with existing constructions,the new 8-variable WPB function outperforms the existing k-weight nonlinearity at values of 3 and 4,reaching 18 and 26,respectively,and the new 16-variable WPB function shows enhanced k-weight nonlinearity at k=13,achieving 160,surpassing the highest value of 152 for the existing constructions.关键词
FLIP/逐重量完美平衡布尔函数/代数次数/重量非线性度Key words
FLIP/weightwise perfectly balanced Boolean function/algebraic degree/weightwise nonlinearity分类
电子信息工程引用本文复制引用
赵庆兰,王富佳,秦宝东..逐重量完美平衡布尔函数的构造[J].通信学报,2025,46(2):97-107,11.基金项目
国家自然科学基金资助项目(No.62372370,No.61902314,No.62072371) The National Natural Science Foundation of China(No.62372370,No.61902314,No.62072371) （No.62372370,No.61902314,No.62072371）
