2005/11/29 by Na Li, Li, Na, Wen‐Feng Qi +2
Computer Science · Engineering · #Coding theory and cryptography #Cryptographic Implementations and Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #cs.CR #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.cs/0511099
arxiv created 2005/11/29 · openalex publication_date 2005/11/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To resist algebraic attack, a Boolean function should possess good algebraic immunity (AI). Several papers constructed symmetric functions with the maximum algebraic immunity \lceil (n)/(2)\rceil . 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 \lceil (n)/(2)\rceil . And we also obtain a necessary condition for the algebraic normal form of a symmetric Boolean function with maximum algebraic immunity.