Constructing odd-variable rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity

— Rotation symmetric Boolean functions (RSBFs) have attracted widespread attention due to their good cryptographic properties. We present a new construction of RSBFs with optimal algebraic immunity on odd number of variables. The nonlinearity of the new function is much higher than other best known RSBFs with optimal algebraic immunity. The algebraic degree of the constructed n-variable RSBF can achieve the upper bound n−1 when n/2 is odd or when n/2 is a power of 2 for n≥11. In addition, the constructed function can possess almost perfect immunity to fast algebraic attacks for n=11,13,15.