Constructing odd-variable RSBFs with optimal algebraic immunity, good nonlinearity and good behavior against fast algebraic attacks

Abstract

Rotation symmetric Boolean functions have raised widespread attention because of the good properties in cryptosystem. This paper presents a new construction of odd-variable rotation symmetric Boolean functions with optimal algebraic immunity. The nonlinearity of the new functions is higher than some existing theoretical constructions of rotation symmetric Boolean functions with optimal algebraic immunity. Further, it is also checked that such functions have almost optimal immunity against fast algebraic attacks for small variables. Besides, the algebraic degree of the constructed functions is also high enough.