通信学报2025，Vol.46Issue(3)：144-150,7.DOI:10.11959/j.issn.1000-436x.2025048
高非线性四谱值和五谱值布尔函数的构造
Construction of highly nonlinear Boolean functions with four-valued and five-valued spectra
摘要
Abstract
Boolean functions with four-valued and five-valued spectra are of special interest for cryptography applica-tions.By modifying bent functions in the Maiorana-McFarland class,a construction of Boolean functions on even num-bers of variables with four-valued and five-valued spectra was presented,and their spectral distributions were deter-mined.The nonlinearity of these functions was proved to be as good as that of semi-bent functions,i.e.,2n-1-2n/2(n was the number of variables),and the algebraic degree could reach any value ranging from 3 to the theoretical upper bound n/2+1.Furthermore,a subclass of the construction was studied,which consisted of Boolean functions with five-valued spectra,the highest algebraic degree n/2+1,and without non-zero linear structures.关键词
布尔函数/四谱值函数/五谱值函数/非线性度/代数次数Key words
Boolean function/four-valued spectra function/five-valued spectra function/nonlinearity/algebraic degree分类
信息技术与安全科学引用本文复制引用
郭飞,王子龙,段明..高非线性四谱值和五谱值布尔函数的构造[J].通信学报,2025,46(3):144-150,7.基金项目
国家自然科学基金资助项目(No.62472438,No.62172319) The National Natural Science Foundation of China(No.62472438,No.62172319) （No.62472438,No.62172319）
