密码学报（中英文）2024，Vol.11Issue(4)：924-944,21.DOI:10.13868/j.cnki.jcr.000717
任意偶变元上代数免疫度最优的平衡旋转对称布尔函数的构造
Construction of Balanced Rotation Symmetric Boolean Functions with Optimal Algebraic Immunity on Arbitrary Even Variables
摘要
Abstract
Rotation symmetric Boolean functions are a class of Boolean functions whose output remains unchanged under the cyclic shift of the input.These functions have received much attention in cryptography because of their special structure and the fact that they include many functions with good cryptographic properties.After the emergence of algebraic attacks,the construction of balanced rotation symmetric Boolean functions with optimal algebraic immunity has become a hot topic in the study of Boolean functions.The study of this topic has been rich in arbitrary odd variables,but has been a challenging work on those in arbitrary even variables.In 2021,Mesnager et al.proposed a construction method that successfully solved this problem,however the nonlinearity of their constructed functions is not high.This paper presents a new construction method of rotation symmetric Boolean functions on arbitrary even variables n,which can ensure that the constructed functions have optimal algebraic immunity and good balancedness,as well as higher nonlinearity than the existing constructions for arbitrary even variables when n is greater than or equal to 8.In addition,when n is not greater than 16,experiments show that those functions have good resistance against fast algebraic attacks,and the algebraic degree can reach the highest values n-1 or the almost highest values n-2.关键词
旋转对称布尔函数/代数次数/代数免疫度/平衡性/非线性度Key words
rotation symmetric Boolean functions/algebraic degree/algebraic immunity/balanced-ness/nonlinearity分类
信息技术与安全科学引用本文复制引用
赵庆兰,李盼,郑东,李梦苒,张建东..任意偶变元上代数免疫度最优的平衡旋转对称布尔函数的构造[J].密码学报（中英文）,2024,11(4):924-944,21.基金项目
国家自然科学基金(61902314)National Natural Science Foundation of China(61902314) （61902314）
