密码学报（中英文）2026，Vol.13Issue(1)：109-121,13.DOI:10.13868/j.cnki.jcr.000841
基于不相交码的严格几乎最优弹性函数构造
Construction of Resilient Boolean Functions with Strictly Almost Optimal Nonlinearity Through Disjoint Linear Codes
摘要
Abstract
Boolean functions are served as crucial nonlinear components in stream cipher systems.To safeguard the entire system against various attacks,such as the best affine approximation attack,correlation attack,and algebraic attack,they need to meet several cryptographic criteria,including high nonlinearity,a certain order of resilience,and good algebraic properties.Nevertheless,there exists a trade-off between the resilience and nonlinearity of Boolean functions.Therefore,constructing resilient Boolean functions with high nonlinearity has always been a significant challenge in the field of cryptographic function design.This study draws inspiration from the traditional Maiorana-McFarland(M-M)class construction approach and utilizes a special class of disjoint code structures to construct a family of Boolean functions with alternating Walsh spectrum distributions.These functions are then cascaded,followed by necessary modifications,ultimately leading to a method for constructing resilient Boolean functions with high nonlinearity.This method can extend balanced functions of k variables(where k≥6)with strictly almost optimal nonlinearity to functions of 3k variables and provides a constructive approach to modifying them into resilient functions without impairing nonlinearity.关键词
布尔函数/不相交谱函数/不相交码/非线性度/弹性Key words
Boolean function/disjoint spectrum function/disjoint linear code/nonlinearity/re-siliency分类
信息技术与安全科学引用本文复制引用
季彦晗,孙玉娟,李路阳..基于不相交码的严格几乎最优弹性函数构造[J].密码学报（中英文）,2026,13(1):109-121,13.基金项目
国家自然科学基金(62272360,62572367) （62272360,62572367）
陕西省自然科学基础研究计划(2023-JC-YB-570)National Natural Science Foundation of China(62272360,62572367) （2023-JC-YB-570）
Natural Science Basic Research Program of Shaanxi Province(2023-JC-YB-570) （2023-JC-YB-570）
