Symmetric Boolean Function with Maximum Algebraic Immunity on Odd Number of Variables
Na Li, Wen-feng Qi
Abstract
To resist algebraic attack, a Boolean function should possess good algebraic immunity (AI). Several papers constructed symmetric functions with the maximum algebraic immunity n2 . In this correspondence we prove that for each odd n, there is exactly one trivial balanced n-variable symmetric Boolean function achieving the algebraic immunity n2 . And we also obtain a necessary condition for the algebraic normal form of a symmetric Boolean function with maximum algebraic immunity.
Create a lesson
Related papers
RedEvoAgent: Automatic Red-Teaming Agent with Experience-Driven Skill Evolution
Junjie Zhang, Hui Liu, Kecheng Chen et al.
Beyond F1: Evaluating Coverage and Failure Recovery in AI Model Security Scanners
Qianlong Lan, Vinothini Pandurangan, Anuj Kaul et al.
When Context Gets Root: Privilege Escalation in LLM Harnesses
Xingbang He, Yuanwei Chen, Yi Qian et al.
Low-ASR Backdoors: Exploiting Attack Success Rate Reduction and Attacker-Defender Asymmetry
Arham Riaz, Ting Yu
SPA: Securing Persistent LLM Agents Across Queries with Plan-First Information-Flow Control
Dylan Girrens, Guangjing Wang
From Security Events to Conflict States: A Three-layer Cyber Defense Scenario Model for Enhanced Cyber Situational Awareness
Miguel Requena Micó, Mario Fernandez-Tarraga, Daniel Díaz-López et al.