A new construction of rotation symmetric Boolean functions with optimal algebraic immunity and higher nonlinearity

In this paper, we present two new kinds of theoretical construction of rotation symmetric Boolean functions with optimal algebraic immunity both on odd variables and on even variables based on ordered integer partitions. Our rotation symmetric Boolean functions are of much better nonlinearity than all the existing theoretical constructions of rotation symmetric Boolean functions with optimal algebraic immunity. Further, the algebraic degrees and the fast algebraic immunities of our rotation symmetric Boolean functions are also high enough in some cases.