The Symmetric Property of Boolean Functions

Abstract

Symmetric property is a special property of Boolean functions, which has attracted much study on it. This chapter presents fast Walsh transforms of symmetric Boolean functions, correlation immunity of symmetric functions, construction of symmetric resilient Boolean functions, and some cryptographic properties of majority functions being a special class of symmetric Boolean functions. The study on the correlation immunity of majority functions shows that majority functions have good asymptotical behavior of correlation immunity, i.e., although they are not correlation immune, they have, however, asymptotical correlation immunity.